Transit time effect and 45° magnetron

Transit time effect

Transit time is the time an electron needs to travel between two electrodes: τ = d/v. At low frequencies τ is much shorter than the signal period and can be ignored. At microwave frequencies τ is comparable to the period, so the electrode voltage changes while the electron is still travelling. In conventional tubes this causes phase lag, loading of the input (input conductance ∝ ω²τ²) and lower gain and efficiency. Microwave tubes such as klystrons and magnetrons use transit time on purpose to bunch electrons.

Magnetron with 45° phase difference between adjacent cavities

For N cavities in mode n, the phase difference is φ = 2πn/N. For 45°, N = 8n: an 8-cavity anode in mode n = 1 (one spoke), or a 16-cavity anode in mode n = 2 (two spokes).

   8-cavity anode, phase of each cavity
              0°
       315° _/ \_ 45°
          /       \
    270° | (cathode) |  90°     B0 axial
          \  spoke  /          E radial
       225° \_ _/ 135°
             180°

Working principles

1. Cross fields: the cathode is at the centre and the anode block (8 cavities) around it. The anode voltage gives a radial E, and a magnet gives an axial B₀ above the Hull cut-off, B₀c = √(8mV₀/e) / [b(1 − a²/b²)]. Without RF, electrons curve back to the cathode.
2. RF pattern: noise starts oscillation in the cavities. In this mode each cavity's slot field lags its neighbour by 45°, so the RF fields in the interaction space form a wave rotating around the cathode once per n RF cycles. Its angular velocity is ω/n.
3. Synchronism (Hartree condition): V₀ and B₀ are set so that the E × B drift of electrons around the cathode matches the angular velocity of the wave.
4. Phase focusing: electrons in the retarding phase of the tangential RF field give energy to the wave and move outward to the anode. Electrons in the accelerating phase take energy, return to the cathode and are removed.
5. Spokes and output: the useful electrons form n rotating spokes (one for 8 cavities). These keep giving energy to the cavities in step, which sustains the oscillation. Power is coupled out by a loop in one cavity.
6. Mode control: because this is not the π-mode (180°), the mode must be chosen by the anode design. Strapping favours π-mode, so a non-π mode like this needs suitable coupling or an injected signal to hold it.

Uses: pulsed radar transmitters, industrial heating and, in amplifier form (cross-field amplifier), radar power stages.